As the rise of mobile computing has made the dominance of Microsoft’s Windows look shaky, some people wonder which alternative operating system will take its place.

A new service launched today by cloud storage startup Box (previously known as Box.net) is intended to prove that it doesn’t really matter. Box founder and CEO Aaron Levie claims that the next decade of computing won’t be defined by one platform, but by the cloud service that can successfully link apps, users, and devices strung out across competing mobile and desktop operating systems.

Levie pitches the service launched today, called OneCloud, as the first step toward that vision. It enables certain business apps for the iPad and iPhone to use Box’s cloud storage instead of a device’s own storage to save and retrieve files.

OneCloud makes it easy for any of those apps to use the same data, and for different people to collaborate on files without using e-mail or some other means to move them between devices. So far, 31 apps have been approved to use OneCloud, including the document-editing app QuickOffice, note-taking app PaperPort Notes, and document-signing app Adobe EchoSign. Users select and install the apps via Box’s own mobile app. Files in Box storage can also be accessed on desktop computers and through a Web browser.

For companies that subscribe to Box, OneCloud also means that business data that would otherwise be invisibly spread across employees’ mobile devices is in one controllable place. “The situation now is that we have people with all of these devices creating personal mini-clouds of data,” says Levie. “We want all the data to go back to one place.” OneCloud will work on Google’s Android mobile operating system in the coming months, he says.

Levie claims that OneCloud shows how cloud storage can become a fundamental layer that all apps use to make data easier to store, share, and control. “For the first time in decades, the market is in flux, and there’s this opportunity to create the next fundamental change in how people work,” says Levie. “We’re sort of building a business operating system.” Box has received $162 million in investment funding and claims more than 10 million users, including large companies such as Procter & Gamble and Balfour Beatty, a construction company.

However, Box isn’t alone—others share Levie’s dream of offering cloud storage as the ultimate helper in a multidevice, multiplatform world.

For example, Apple’s iCloud launched last June. Steve Jobs pitched it using rhetoric similar to Levie’s. However the service has disappointed some Apple customers because it only synchronizes data between devices from certain Apple apps, and is focused on moving data from device to device, rather than acting as a cloud data store.

Fellow startup Dropbox is another competitor to Box. Dropbox is better funded but more focused on consumers, and launched its service for businesses only late last year. Third-party apps can make use of Dropbox storage in a similar way to Box’s OneCloud apps, but the company has been less active in promoting the apps that do (read an in-depth interview with Dropbox founder Drew Houston).

Levie says his company is also working on making its storage smarter. In the future, companies with data in Box will be able to take advantage of services such as in-depth search or virus scanning, or scan their files to enforce compliance with regulations, such as those that restrict some financial companies from making forward-looking statements.

Whether or not Box or similar services ever become as important as operating systems, it is clear that they can boost the efficiency of organizations, and there is a need for services that unite our many computers, says Derek Brink, an analyst with Aberdeen Group. Many people now use the free versions of Dropbox or Box to handle their work data. “Users take advantage of the consumer-oriented solutions because they’re trying to get their jobs done,” he says. “Until the enterprise provides them with a ‘sanctioned’ alternative, they’re going to find a way to use the best and most convenient solutions available.”

Brink adds that Box’s OneCloud could help businesses gain the control administrators crave over mobile devices, which are seen as a security risk. “Many enterprises I’ve spoken to express the view that their biggest concern is with the persistence of [business] data and applications on the mobile devices,” he says. “That is, if they could manage the apps and data, then they wouldn’t necessarily care about managing the devices.”

Brink notes, however, that Box isn’t alone in trying to bridge the divide between easy-to-use services for people struggling with multiple devices and the control that businesses want. He singles out Accellion, which recently launched a Dropbox-like service targeted at businesses, and says that even Microsoft could yet become a competitor.

Levie dismisses that last threat in the same way Dropbox’s founders have, saying that a “neutral” third party will be more successful at working across platforms operated by Microsoft and its competitors Apple and Google.